Finite Group Databasebeta

← C22×C3×#107 #84772

Subgroups — C22×C3×#107 #84772

Order 384.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C8C211yesmaximal, characteristic
2C22×C3×C4⋊C4C212yesmaximal
3C2×C3×#107C2112yesmaximal, direct product factor
4C22×#107C311yesmaximal, characteristic, direct product factor, Sylow
5C23×C3×C4—22no—
6C23×C3×C4C2211yescharacteristic
7C22×C3×C8C418yescomplemented
8C22×C3×C8C2216yes—
9C2×C3×C4⋊C4—26no—
10C2×C3×C4⋊C4C22112yes—
11C3×#107C22116yesdirect product factor
12C23×C8C2×C311yescharacteristic
13C22×C4⋊C4C2×C312yes—
14C2×#107C2×C3112yesdirect product factor
15C24×C3D411yescharacteristic
16C22×C3×C4—212no—
17C22×C3×C4—48no—
18C22×C3×C4C2×C414yes—
19C22×C3×C4D413yes—
20C22×C3×C4Q814yes—
21C22×C3×C4C2313yes—
22C2×C3×C8C2×C4124yescomplemented
23C2×C3×C8C2314yes—
24C3×C4⋊C4—212no—
25C3×C4⋊C4C2318yes—
26C23×C4—22no—
27C23×C4C22×C311yescharacteristic
28C22×C8C3×C418yescomplemented
29C22×C8C22×C316yes—
30C2×C4⋊C4—26no—
31C2×C4⋊C4C22×C3112yes—
32#107C22×C3116yesdirect product factor
33C23×C3C4⋊C414yes—
34C23×C3D814yes—
35C23×C3Q1614yes—
36C23×C3C2×D413yes—
37C2×C3×C4—28no—
38C2×C3×C4—424no—
39C2×C3×C4C4⋊C4112yes—
40C2×C3×C4C22×C416yes—
41C2×C3×C4C2×D413yes—
42C2×C3×C4C2×Q816yes—
43C2×C3×C4C2411yescharacteristic
44C3×C8C22×C418yescomplemented
45C24C3×D411yescharacteristic
46C22×C4—212no—
47C22×C4—48no—
48C22×C4C2×C3×C414yes—
49C22×C4C3×D413yes—
50C22×C4C3×Q814yes—
51C22×C4C23×C313yes—
52C2×C8C2×C3×C4124yescomplemented
53C2×C8C23×C314yes—
54C4⋊C4—212no—
55C4⋊C4C23×C318yes—
56C22×C3#107116yesdirect product factor
57C22×C3C2×C4⋊C416yes—
58C22×C3C2×D816yes—
59C22×C3C2×Q1616yes—
60C22×C3C22×D411yescharacteristic
61C3×C4—48no—
62C3×C4C2×C4⋊C416yes—
63C3×C4C23×C411yescharacteristic
64C3×C4C22×Q811yescharacteristic
65C23C3×C4⋊C414yes—
66C23C3×D814yes—
67C23C3×Q1614yes—
68C23C2×C3×D413yes—
69C2×C4—28no—
70C2×C4—424no—
71C2×C4C3×C4⋊C4112yes—
72C2×C4C22×C3×C416yes—
73C2×C4C2×C3×D413yes—
74C2×C4C2×C3×Q816yes—
75C2×C4C24×C311yescharacteristic
76C8C22×C3×C418yescomplemented
77C2×C3C2×#107112yesdirect product factor
78C2×C3C22×C4⋊C411yescharacteristic
79C2×C3C22×D811yescharacteristic
80C2×C3C22×Q1611yescharacteristic
81C22C3×#107116yesdirect product factor
82C22C2×C3×C4⋊C416yes—
83C22C2×C3×D816yes—
84C22C2×C3×Q1616yes—
85C22C22×C3×D411yescharacteristic
86C4—48no—
87C4C2×C3×C4⋊C416yes—
88C4C23×C3×C411yescharacteristic
89C4C22×C3×Q811yescharacteristic
90C3C22×#10711yescharacteristic, direct product factor, Sylow
91C2C2×C3×#107112yesdirect product factor
92C2C22×C3×C4⋊C411yescharacteristic
93C2C22×C3×D811yescharacteristic
94C2C22×C3×Q1611yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3D4
commutatorC4C23×C3×C4
Frattini, cosocleC2×C4C24×C3
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C3 ◁ C23×C3×C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C3×#107C2direct (N × H)
4. C22×#107C3direct (N × H)
7. C22×C3×C8C4semidirect
11. C3×#107C22direct (N × H)
14. C2×#107C2×C3direct (N × H)
22. C2×C3×C8C2×C4semidirect
28. C22×C8C3×C4semidirect
32. #107C22×C3direct (N × H)
44. C3×C8C22×C4semidirect
52. C2×C8C2×C3×C4semidirect
56. C22×C3#107direct (N × H)
76. C8C22×C3×C4semidirect
77. C2×C3C2×#107direct (N × H)
81. C22C3×#107direct (N × H)
90. C3C22×#107direct (N × H)
91. C2C2×C3×#107direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C3×C82
C22×C3×C4⋊C42
C2×C3×#1072
C22×#1073